First off, is this an oxymoron? Is it impossible to have an abusive character that is at least sympathetic? If not, has it been done before in literature? This has been something that has been bouncing around within my stories for awhile. Right now, I have at least two that involve abusive mothers(I mean like beat their sons until they bleed type of abuse, not just verbal) and both stories depend heavily on them being at least somewhat sympathetic.
Abusers were often themselves abused. An abuser who knows he or she is abusive, and who tries desperately to break the cycle might be sympathetic. But it is still a choice, and many readers familiar with abuse will never find the abuser sympathetic. And abuse is far more prevalent than you probably think.
I think it's quite common, considering the psychology of such relationships can cause them to be created again, and how many relationships derail into them, but keep on because of times in the past. Anyway, thanks, great stuff to chew on.
To both questions: absolutely yes. What hasn't been done yet? Can't think of any professional examples off the top of my head but I've seen it done countless times - and I've written about characters like this too.
If the abuser is one of the main characters, showing a sympathetic side of her will make her a rounded character. Dig deeper and find out why and when she is abusive and sympathetic.
I knew a friend once who was abused. [This is coming to me in pieces]. I remember feeling very sorry for him. Because he tried. He tried so hard to not be the person that the abuser was to him. But the more he tried, the more he failed and the more he failed the more he became abusive. Also even self destructive. And I think the self destructive bit is where you'll find the most sympathetic part of an abuser. My friend felt he needed to be punished. Either he sought out people to abuse him or he sought out people to abuse them. But in either way he ended up destroyed and broken. He committed suicide. But I remember him even abusing himself at times.